A reverse mortgage is made with a balance not to exceed $$300,000$ on a property now valued at $$700,000.$ The loan calls for monthly payments to be made to the borrower for $120$ months at an interest rate of $6$ percent.

Required:

a$.$ What will the monthly payments be$?$

b$.$ What will be the loan balance at the end of year $3?$

c$.$ Assume that the borrower must have monthly draws of $$2,000$ for the first $50$ months of the loan. Remaining draws from months $51$ to $120$ must be determined so that the $$300,000$ maximum is not exceeded in month $120.$ What will draws by the borrower be during months $51$ to $120?$